### Speaker

Mr
Piotr Sierant
(Jagiellonian University in Kraków)

### Description

This contribution is based mainly on [1]. Many-body localization for a system of
bosons trapped in a one dimensional lattice is discussed.
Two models that may be realized for cold atoms in optical lattices are considered.
The first one is Bose--Hubbard model with a random on--site potential
$ H = -J \sum_{\langle i,j \rangle} \hat{a}^{+}_i\hat{a}_j + \frac{ U }{2} \sum_i \hat{n}_i (\hat{n}_i - 1) + \sum_i \mu_i \hat{n}_i $
where $a_i^{+}$ and $a_i$ are operators creating and annihilating boson at site
$i$ of the lattice, $J$ and $U$ are respectively tunneling amplitude and interaction strength
and $\mu_i$ is a random on--site potential distributed uniformly in interval $[-W,W]$.
The random on--site potential model is compared with random interactions model [2-3]
$ H = -J \sum_{\langle i,j \rangle} \hat{a}^{+}_i\hat{a}_j +
\frac{ 1 }{2} \sum_i U_i \hat{n}_i (\hat{n}_i - 1) $
where $U_i \in [0,U]$ is random interaction strength.
While the origin and character of the disorder in both systems is different they show interesting
similar properties. In particular, many-body localization appears for a sufficiently large disorder
strengths $W$ and $U$ as verified by a time evolution of initial density wave states as well as
using statistical
properties of energy levels for small system sizes. Starting with different initial states,
we observe that the localization properties are energy-dependent which reveals an inverted
many-body localization edge in both systems -- that finding is also verified by statistical
analysis of energy spectrum -- see Fig.~1.
Moreover, we consider computationally challenging regime of
transition between many body localized and extended phases where we observe a characteristic
algebraic decay of density correlations which may be attributed to subdiffusion
(and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered
Bose-Hubbard models is compared with the slowing-down of the time evolution of the clean system
at large interactions.
[1] P. Sierant and J. Zakrzewski,
Many-body localization of bosons in optical lattices,
New J. Phys. $\textbf{20}$ 043032 (2018)
[2] Piotr Sierant, Dominique Delande, and Jakub Zakrzewski,
Many-body localization due to random interactions,
Phys. Rev. A $\textbf{95}$, 021601 (2017)
[3] Piotr Sierant, Dominique Delande, Jakub Zakrzewski,
Many-body localization for randomly interacting bosons,
Acta Physica Polonica A $\textbf{132}$, 1707 (2017)

### Primary author

Mr
Piotr Sierant
(Jagiellonian University in Kraków)

### Co-author

Mr
Jakub Zakrzewski
(Jagiellonian University in Kraków)